The average annual return over the period 1886-2006 for stocks that comprise the S&P 500 is 10.5%,and the standard deviation of returns is 18.5%.Based on these numbers,what is a 95% confidence interval for 2007 returns?
A)-18.5%,18.5%
B)-10%,10%
C)-26.5%,47.5%
D)-37%,37%
E)-8%,29%

Question

Quizplus · Accepted Answer

To calculate a 95% confidence interval for the returns, we use the formula: average ± (1.96 * standard deviation). Plugging in the numbers: 10.5% ± (1.96 * 18.5%) = 10.5% ± 36.26%, which gives us the interval from -25.76% to 46.76%. Rounding these to the nearest half percent gives us -26.5% to 47.5%, which matches option C.

The Average Annual Return Over the Period 1886-2006 for Stocks